Trump told reporters he was "looking at Larry Kudlow very strongly" and noted that while he and Kudlow didn't agree on the president's recent decision to impose tariffs on steel and aluminum imports, Kudlow's views would be helpful to him.

"I think Larry has a very good chance," Trump said. He noted that Kudlow, an advocate of free trade, is a longtime friend who had been an early supporter of Trump's 2016 presidential campaign.

Kudlow is CNBC's senior contributor and was previously the host of CNBC's prime-time "The Kudlow Report." He served in the Office of Management and Budget during President Ronald Reagan's administration.

Trump has been considering a potential replacement for Cohn as director of the National Economic Council. In addition to Kudlow, the potential successors include Chris Liddell, who serves as the White House's director of strategic initiatives, and Shahira Knight, Cohn's deputy at the National Economic Council and a key architect of the president's tax overhaul law.

The president said last week that Cohn, the former top Goldman Sachs executive, was likely to return to his administration in the future. Cohn strongly opposed the president's plan to slap tariffs on the steel and aluminum imports and worked to provide exemptions to U.S. allies such as Canada and Mexico.

Cohn played a central role in helping Trump enact a sweeping tax overhaul law, coordinating with members of Congress. His departure has been worrisome for Capitol Hill Republicans and business groups who have been concerned that Trump may install more protectionist economic policies amid a renegotiation of the North American Free Trade Agreement.